Results for 'mathematical models'

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  1. Mathematical models: Questions of trustworthiness.Adam Morton - 1993 - British Journal for the Philosophy of Science 44 (4):659-674.
    I argue that the contrast between models and theories is important for public policy issues. I focus especially on the way a mathematical model explains just one aspect of the data.
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  2.  2
    Towards a simple mathematical model for the legal concept of balancing of interests.Frederike Zufall, Rampei Kimura & Linyu Peng - forthcoming - Artificial Intelligence and Law:1-21.
    We propose simple nonlinear mathematical models for the legal concept of balancing of interests. Our aim is to bridge the gap between an abstract formalisation of a balancing decision while assuring consistency and ultimately legal certainty across cases. We focus on the conflict between the rights to privacy and to the protection of personal data in Art. 7 and Art. 8 of the EU Charter of Fundamental Rights (EUCh) against the right of access to information derived from Art. (...)
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  3. Mathematical Modelling and Contrastive Explanation.Adam Morton - 1990 - Canadian Journal of Philosophy 20 (Supplement):251-270.
    Mathematical models provide explanations of limited power of specific aspects of phenomena. One way of articulating their limits here, without denying their essential powers, is in terms of contrastive explanation.
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  4. Mathematical models and reality: A constructivist perspective. [REVIEW]Christian Hennig - 2010 - Foundations of Science 15 (1):29-48.
    To explore the relation between mathematical models and reality, four different domains of reality are distinguished: observer-independent reality, personal reality, social reality and mathematical/formal reality. The concepts of personal and social reality are strongly inspired by constructivist ideas. Mathematical reality is social as well, but constructed as an autonomous system in order to make absolute agreement possible. The essential problem of mathematical modelling is that within mathematics there is agreement about ‘truth’, but the assignment of (...)
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  5. A Mathematical Model of Aristotle’s Syllogistic.John Corcoran - 1973 - Archiv für Geschichte der Philosophie 55 (2):191-219.
    In the present article we attempt to show that Aristotle's syllogistic is an underlying logiC which includes a natural deductive system and that it isn't an axiomatic theory as had previously been thought. We construct a mathematical model which reflects certain structural aspects of Aristotle's logic. We examine the relation of the model to the system of logic envisaged in scattered parts of Prior and Posterior Analytics. Our interpretation restores Aristotle's reputation as a logician of consummate imagination and skill. (...)
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  6.  65
    Mathematical models of biological patterns: Lessons from Hamilton’s selfish herd.Christopher Pincock - 2012 - Biology and Philosophy 27 (4):481-496.
    Mathematical models of biological patterns are central to contemporary biology. This paper aims to consider what these models contribute to biology through the detailed consideration of an important case: Hamilton’s selfish herd. While highly abstract and idealized, Hamilton’s models have generated an extensive amount of research and have arguably led to an accurate understanding of an important factor in the evolution of gregarious behaviors like herding and flocking. I propose an account of what these models (...)
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  7.  58
    A Mathematical Model of Juglar Cycles and the Current Global Crisis.Leonid Grinin, Andrey Korotayev & Sergey Malkov - 2010 - In Leonid Grinin, Peter Herrmann, Andrey Korotayev & Arno Tausch (eds.), History & Mathematics: Processes and Models of Global Dynamics.
    The article presents a verbal and mathematical model of medium-term business cycles (with a characteristic period of 7–11 years) known as Juglar cycles. The model takes into account a number of approaches to the analysis of such cycles; in the meantime it also takes into account some of the authors' own generalizations and additions that are important for understanding the internal logic of the cycle, its variability and its peculiarities in the present-time conditions. The authors argue that the most (...)
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  8. A Mathematical Model of Dignāga’s Hetu-cakra.Aditya Kumar Jha - 2020 - Journal of the Indian Council of Philosophical Research 37 (3):471-479.
    A reasoned argument or tarka is essential for a wholesome vāda that aims at establishing the truth. A strong tarka constitutes of a number of elements including an anumāna based on a valid hetu. Several scholars, such as Dharmakīrti, Vasubandhu and Dignāga, have worked on theories for the establishment of a valid hetu to distinguish it from an invalid one. This paper aims to interpret Dignāga’s hetu-cakra, called the wheel of grounds, from a modern philosophical perspective by deconstructing it into (...)
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  9.  29
    Causality, mathematical models and statistical association: dismantling evidence‐based medicine.R. Paul Thompson - 2010 - Journal of Evaluation in Clinical Practice 16 (2):267-275.
  10. Mathematical models of dialogue.C. L. Hamblin - 1971 - Theoria 37 (2):130-155.
  11.  13
    Mathematical Models and Robustness Analysis in Epistemic Democracy: A Systematic Review of Diversity Trumps Ability Theorem Models.Ryota Sakai - 2020 - Philosophy of the Social Sciences 50 (3):195-214.
    This article contributes to the revision of the procedure of robustness analysis of mathematical models in epistemic democracy using the systematic review method. It identifies the drawbacks of robustness analysis in epistemic democracy in terms of sample universality and inference from samples with the same results. To exemplify the effectiveness of systematic review, this article conducted a pilot review of diversity trumps ability theorem models, which are mathematical models of deliberation often cited by epistemic democrats. (...)
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  12. A Mathematical Model of Divine Infinity.Eric Steinhart - 2009 - Theology and Science 7 (3):261-274.
    Mathematics is obviously important in the sciences. And so it is likely to be equally important in any effort that aims to understand God in a scientifically significant way or that aims to clarify the relations between science and theology. The degree to which God has any perfection is absolutely infinite. We use contemporary mathematics to precisely define that absolute infinity. For any perfection, we use transfinite recursion to define an endlessly ascending series of degrees of that perfection. That series (...)
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  13. Mathematics, models and Zeno's paradoxes.Joseph S. Alper & Mark Bridger - 1997 - Synthese 110 (1):143-166.
    A version of nonstandard analysis, Internal Set Theory, has been used to provide a resolution of Zeno's paradoxes of motion. This resolution is inadequate because the application of Internal Set Theory to the paradoxes requires a model of the world that is not in accordance with either experience or intuition. A model of standard mathematics in which the ordinary real numbers are defined in terms of rational intervals does provide a formalism for understanding the paradoxes. This model suggests that in (...)
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  14. Mathematics, Models, and Modality: Selected Philosophical Essays.John P. Burgess - 2008 - Cambridge University Press.
    John Burgess is the author of a rich and creative body of work which seeks to defend classical logic and mathematics through counter-criticism of their nominalist, intuitionist, relevantist, and other critics. This selection of his essays, which spans twenty-five years, addresses key topics including nominalism, neo-logicism, intuitionism, modal logic, analyticity, and translation. An introduction sets the essays in context and offers a retrospective appraisal of their aims. The volume will be of interest to a wide range of readers across philosophy (...)
     
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  15.  40
    A mathematical model for simple learning.Robert R. Bush & Frederick Mosteller - 1951 - Psychological Review 58 (5):313-323.
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  16. A Mathematical Model of Quantum Computer by Both Arithmetic and Set Theory.Vasil Penchev - 2020 - Information Theory and Research eJournal 1 (15):1-13.
    A practical viewpoint links reality, representation, and language to calculation by the concept of Turing (1936) machine being the mathematical model of our computers. After the Gödel incompleteness theorems (1931) or the insolvability of the so-called halting problem (Turing 1936; Church 1936) as to a classical machine of Turing, one of the simplest hypotheses is completeness to be suggested for two ones. That is consistent with the provability of completeness by means of two independent Peano arithmetics discussed in Section (...)
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  17. Mathematical Models of Abstract Systems: Knowing abstract geometric forms.Jean-Pierre Marquis - 2013 - Annales de la Faculté des Sciences de Toulouse 22 (5):969-1016.
    Scientists use models to know the world. It i susually assumed that mathematicians doing pure mathematics do not. Mathematicians doing pure mathematics prove theorems about mathematical entities like sets, numbers, geometric figures, spaces, etc., they compute various functions and solve equations. In this paper, I want to exhibit models build by mathematicians to study the fundamental components of spaces and, more generally, of mathematical forms. I focus on one area of mathematics where models occupy a (...)
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  18.  31
    A mathematical model of Churchmanian inquiring systems with special reference to Popper's measures for?The Severity of Tests?Ian I. Mitroff, Frederick Betz & Richard O. Mason - 1970 - Theory and Decision 1 (2):155-178.
    Through the use of Bayesian probability theory and Communication theory, a formal mathematical model of a Churchmanian Dialectical Inquirer is developed. The Dialectical Inquirer is based on Professor C. West Churchman's novel interpretation and application of Hegelian dialectics to decision theory. The result is not only the empirical application of dialectical inquiry but also its empirical (i.e., scientific) investigation. The Dialectical Inquirer is seen as especially suited to problems in strategic policy formation and in decision theory. Finally, specific application (...)
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  19.  43
    Mathematics, Models, and Modality.Roy T. Cook - 2010 - History and Philosophy of Logic 31 (3):287-289.
    John P. Burgess, Mathematics, Models, and Modality: Selected Philosophical Essays. Cambridge: Cambridge University Press, 2008. xiii + 301 pp. $90.00, £50.00. ISBN 978-0-521-88034-3. Adobe eBook, $...
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  20. Mathematical Models of Time as a Heuristic Tool.Emiliano Ippoliti - 2006 - In Lorenzo Magnani & Claudia Casadio (eds.), Model Based Reasoning in Science and Technology. Logical, Epistemological, and Cognitive Issues. Springer Verlag.
    This paper sets out to show how mathematical modelling can serve as a way of ampliating knowledge. To this end, I discuss the mathematical modelling of time in theoretical physics. In particular I examine the construction of the formal treatment of time in classical physics, based on Barrow’s analogy between time and the real number line, and the modelling of time resulting from the Wheeler-DeWitt equation. I will show how mathematics shapes physical concepts, like time, acting as a (...)
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  21.  31
    A Mathematical Model of Prediction-Driven Instability: How Social Structure Can Drive Language Change. [REVIEW]W. Garrett Mitchener - 2011 - Journal of Logic, Language and Information 20 (3):385-396.
    I discuss a stochastic model of language learning and change. During a syntactic change, each speaker makes use of constructions from two different idealized grammars at variable rates. The model incorporates regularization in that speakers have a slight preference for using the dominant idealized grammar. It also includes incrementation: The population is divided into two interacting generations. Children can detect correlations between age and speech. They then predict where the population’s language is moving and speak according to that prediction, which (...)
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  22. Mathematical models of games of chance: Epistemological taxonomy and potential in problem-gambling research.Catalin Barboianu - 2015 - UNLV Gaming Research and Review Journal 19 (1):17-30.
    Games of chance are developed in their physical consumer-ready form on the basis of mathematical models, which stand as the premises of their existence and represent their physical processes. There is a prevalence of statistical and probabilistic models in the interest of all parties involved in the study of gambling – researchers, game producers and operators, and players – while functional models are of interest more to math-inclined players than problem-gambling researchers. In this paper I present (...)
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  23.  90
    Mathematical Models in Newton’s Principia: A New View of the “Newtonian Style”.Steffen Ducheyne - 2005 - International Studies in the Philosophy of Science 19 (1):1 – 19.
    In this essay I argue against I. Bernard Cohen's influential account of Newton's methodology in the Principia: the 'Newtonian Style'. The crux of Cohen's account is the successive adaptation of 'mental constructs' through comparisons with nature. In Cohen's view there is a direct dynamic between the mental constructs and physical systems. I argue that his account is essentially hypothetical-deductive, which is at odds with Newton's rejection of the hypothetical-deductive method. An adequate account of Newton's methodology needs to show how Newton's (...)
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  24.  3
    A Mathematical Model of the Transmission Dynamics of Bovine Schistosomiasis with Contaminated Environment.Jean M. Tchuenche, Shirley Abelman & Solomon Kadaleka - 2022 - Acta Biotheoretica 70 (1):1-28.
    Schistosomiasis, a vector-borne chronically debilitating infectious disease, is a serious public health concern for humans and animals in the affected tropical and sub-tropical regions. We formulate and theoretically analyze a deterministic mathematical model with snail and bovine hosts. The basic reproduction number R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document} is computed and used to investigate the local stability of the model’s steady states. Global stability of the endemic equilibrium is carried out by constructing a suitable Lyapunov (...)
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  25.  5
    A Mathematical Model of the Tuberculosis Epidemic.Ally Yeketi Ayinla, Wan Ainun Mior Othman & Musa Rabiu - 2021 - Acta Biotheoretica 69 (3):225-255.
    Tuberculosis has continued to retain its title as “the captain among these men of death”. This is evident as it is the leading cause of death globally from a single infectious agent. TB as it is fondly called has become a major threat to the achievement of the sustainable development goals and hence require inputs from different research disciplines. This work presents a mathematical model of tuberculosis. A compartmental model of seven classes was used in the model formulation comprising (...)
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  26. A Mathematical Model of Life and Living.Li-kung Shaw - 1972 - Buenos Aires, Libreria Inglesa.
    [v. 1. Basic theories]--v. 2. Applications.--v. 3. Theory of plants and other essays.
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  27. A Mathematical Model of Human Life.Li-Kung Shaw - 1959 - Rosario, Argentina.
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  28.  36
    A Mathematical Model of Rift Valley Fever with Human Host.Saul C. Mpeshe, Heikki Haario & Jean M. Tchuenche - 2011 - Acta Biotheoretica 59 (3):231-250.
    Rift Valley Fever is a vector-borne disease mainly transmitted by mosquito. To gain some quantitative insights into its dynamics, a deterministic model with mosquito, livestock, and human host is formulated as a system of nonlinear ordinary differential equations and analyzed. The disease threshold $$\mathcal{R}_0$$ is computed and used to investigate the local stability of the equilibria. A sensitivity analysis is performed and the most sensitive model parameters to the measure of initial disease transmission $$\mathcal{R}_0$$ and the endemic equilibrium are determined. (...)
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  29.  7
    A Mathematical Model for Alternation of Polygamy and Parthenogenesis: Stability Versus Efficiency and Analogy with Parasitism.Jean-Pierre Françoise, Philippe Lherminier & Evariste Sanchez-Palencia - 2016 - Acta Biotheoretica 64 (4):537-552.
    The present work is a contribution to the understanding of the sempiternal problem of the “burden of factor two” implied by sexual reproduction versus asexual one, as males are energy consumers not contributing to the production of offspring. We construct a deterministic mathematical model in population dynamics where a species enjoys both sexual and parthenogenetic capabilities of reproduction and lives on a limited resource. We then show how polygamy implies instability of a parthenogenetic population with a small number of (...)
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  30.  6
    A Mathematical Model of How People Solve Most Variants of the Number‐Line Task.Dale J. Cohen, Daryn Blanc‐Goldhammer & Philip T. Quinlan - 2018 - Cognitive Science 42 (8):2621-2647.
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  31.  58
    Mathematical models of foreign policy decision-making: Compensatory vs. noncompensatory.Alex Mintz, Nehemia Geva & Karl Derouen - 1994 - Synthese 100 (3):441 - 460.
    There are presently two leading foreign policy decision-making paradigms in vogue. The first is based on the classical or rational model originally posited by von Neumann and Morgenstern to explain microeconomic decisions. The second is based on the cybernetic perspective whose groundwork was laid by Herbert Simon in his early research on bounded rationality. In this paper we introduce a third perspective — thepoliheuristic theory of decision-making — as an alternative to the rational actor and cybernetic paradigms in international relations. (...)
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  32.  17
    A mathematical model of uterine dynamics and its application to human parturition.C. Vauge, B. Carbonne, E. Papiernik & F. Ferré - 2000 - Acta Biotheoretica 48 (2):95-105.
    We have developed a simple mathematical model with three physiologically significant states to describe the changes in intrauterine pressure associated with a contraction during human parturition. The myometrium is modelled as a set of smooth muscle cells, each of which is in one of three states (quiescent, contracted, refractory) at a given time. These states are occupied according to a cycle governed by three temporal parameters. The solutions of the equations describing the model show an oscillatory behavior for particular (...)
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  33. Mathematical models of cognitive space and time.Joseph Goguen - 2006 - In D. Andler, M. Okada & I. Watanabe (eds.), Reasoning and Cognition. pp. 125--128.
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  34.  23
    Mathematical models of HIV pathogenesis and treatment.Dominik Wodarz & Martin A. Nowak - 2002 - Bioessays 24 (12):1178-1187.
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  35.  4
    Mathematical Models, Rational Choice, and the Search for Cold War Culture.Paul Erickson - 2010 - Isis 101 (2):386-392.
  36.  15
    Mathematical Models of Foreign Policy Decision-Making: Compensatory vs. Noncompensatory.Alex Mintz, Nehemia Geva & Karl Derouen Jr - 1994 - Synthese 100 (3):441 - 460.
    There are presently two leading foreign policy decision-making paradigms in vogue. The first is based on the classical or rational model originally posited by von Neumann and Morgenstern to explain microeconomic decisions. The second is based on the cybernetic perspective whose groundwork was laid by Herbert Simon in his early research on bounded rationality. In this paper we introduce a third perspective -- the poliheuristic theory of decision-making -- as an alternative to the rational actor and cybernetic paradigms in international (...)
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  37. A Mathematical Model for Info-computationalism.A. C. Ehresmann - 2014 - Constructivist Foundations 9 (2):235-237.
    Open peer commentary on the article “Info-computational Constructivism and Cognition” by Gordana Dodig-Crnkovic. Upshot: I propose a mathematical approach to the framework developed in Dodig-Crnkovic’s target article. It points to an important property of natural computation, called the multiplicity principle (MP), which allows the development of increasingly complex cognitive processes and knowledge. While local dynamics are classically computable, a consequence of the MP is that the global dynamics is not, thus raising the problem of developing more elaborate computations, perhaps (...)
     
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  38.  6
    A mathematical model and an electronic model for learning.L. Benjamin Wyckoff - 1954 - Psychological Review 61 (2):89-97.
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  39.  12
    Mathematical model and simulation of retina and tectum opticum of lower vertebrates.U. an der Heiden & G. Roth - 1987 - Acta Biotheoretica 36 (3):179-212.
    The processing of information within the retino-tectal visual system of amphibians is decomposed into five major operational stages, three of them taking place in the retina and two in the optic tectum. The stages in the retina involve a spatially local high-pass filtering in connection to the perception of moving objects, separation of the receptor activity into ON- and OFF-channels regarding the distinction of objects on both light and dark backgrounds, spatial integration via near excitation and far-reaching inhibition. Variation of (...)
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  40.  35
    Mathematical Modelling and Ideology in the Economics Academy: competing explanations of the failings of the modern discipline?Tony Lawson - 2012 - Economic Thought 1 (1).
    The widespread and long-lived failings of academic economics are due to an over-reliance on largely inappropriate mathematical methods of analysis. This is an assessment I have long maintained. Many heterodox economists, however, appear to hold instead that the central problem is a form of political-economic ideology. Specifically, it is widely contended in heterodox circles that the discipline goes astray just because so many economists are committed to a portrayal of the market economy as a smoothly or efficiently functioning system (...)
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  41.  35
    A mathematical model of the equilibrium distribution of chemical complexes and the biological effects of chemical binding.L. D. Homer - 1967 - Acta Biotheoretica 17 (3):125-138.
    A general equation is derived describing the concentration of all possible complexes of a central molecule with a set of ligands bound to the central molecule. This deduction allows the reaction rate constants for the binding of a given molecule to the central molecule to depend on the species of molecules already bound and the location of the molecules already bound. The model thus allows for structural alteration of the central molecule by binding. Functions describing the concentration dependence of any (...)
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  42. Mathematical model and simulation of retina and tectum opticum of lower vertebrates.U. Heiden & G. Roth - 1987 - Acta Biotheoretica 36 (3).
    The processing of information within the retino-tectal visual system of amphibians is decomposed into five major operational stages, three of them taking place in the retina and two in the optic tectum. The stages in the retina involve (i) a spatially local high-pass filtering in connection to the perception of moving objects, (ii) separation of the receptor activity into ON- and OFF-channels regarding the distinction of objects on both light and dark backgrounds, (iii) spatial integration via near excitation and far-reaching (...)
     
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  43.  14
    Mathematical Model of the Dynamics of Fish, Waterbirds and Tourists in the Djoudj National Park, Senegal.Abdou Sène & Oumar Diop - 2016 - Acta Biotheoretica 64 (4):447-468.
    In the present paper, we propose and analyze a harvested predator–prey model that incorporates the dynamics of tourists in the Djoudj National Park of Birds, Senegal. The model describes the impact of migration of waterbirds and seasonal fishing on the global coexistence of species in the site of the Djoudj. By the Mahwin continuation theorem of coincidence degree theory, we investigate the existence of a positive periodic solution. The global asymptotic stability is discussed by constructing a suitable Lyapunov functional. Some (...)
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  44.  17
    A mathematical model for the spontaneous contractions of the isolated uterine smooth muscle from patients receiving progestin treatment.Christian Vauge, Thérèse-Marie Mignot, Brigitte Paris, Michelle Breuiller-Fouché, Charles Chapron, Michel Attoui & Françoise Ferré - 2003 - Acta Biotheoretica 51 (1):19-34.
    The in vitro spontaneous contractions of human myometrium samples can be described using a phenomenological model involving different cell states and adjustable parameters. In patients not receiving hormone treatment, the dynamic behavior could be described using a three-state model similar to the one we have already used to explain the oscillations of intra-uterine pressure during parturition. However, the shape of the spontaneous contractions of myometrium from patients on progestin treatment was different, due to a two-step relaxation regime including a latched (...)
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  45.  7
    A Mathematical Model for the Transmission Dynamics of Lymphatic Filariasis with Intervention Strategies.S. M. Simelane, P. M. Mwamtobe, S. Abelman & J. M. Tchuenche - 2019 - Acta Biotheoretica 68 (3):297-320.
    This manuscript considers the transmission dynamics of lymphatic filariasis with some intervention strategies in place. Unlike previously developed models, our model takes into account both the exposed and infected classes in both the human and mosquito populations, respectively. We also consider vaccinated, treated and recovered humans in the presented model. The global dynamics of the proposed model are completely determined by the basic and effective reproduction numbers. We then use Lyapunov function theory to find the sufficient conditions for global (...)
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  46.  16
    A mathematical model for the shape of the hooks of cestodae.L. Dujardin & T. Duriez - 1995 - Acta Biotheoretica 43 (3):217-225.
    The shape of hooks is of a taxonomic significance for cestoda. In order to characterize shape through numbers, a mathermatical model of drawings in two-dimensional space is proposed. This model is a synthetic one: first, it uses a large number of points on the edge of a hook-drawing as data; secondly, it enables to draw a specific hook by means of a computer after the parameters have been extracted from the data. The method does not use landmarks and therefore avoids (...)
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  47. Mathematical models of social interaction.Anatol Rapoport - 1963 - In D. Luce (ed.), Handbook of Mathematical Psychology. John Wiley & Sons.. pp. 2--493.
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  48.  27
    Mathematical modelling of an ischemic stroke: An integrative approach.Marie-Aimée Dronne, Jean-Pierre Boissel, Emmanuel Grenier, Hervé Gilquin, Michel Cucherat, Marc Hommel, Emmanuel Barbier & Giampiero Bricca - 2004 - Acta Biotheoretica 52 (4):255-272.
    Understanding the mechanisms and the time and spatial evolution of penumbra following an ischemic stroke is crucially important for developing therapeutics aimed at preventing this area from evolving towards infarction. To help in integrating the available data, we decided to build a formal model. We first collected and categorised the major available evidence from animal models and human observations and summarized this knowledge in a flow-chart with the potential key components of an evolving stroke. Components were grouped in ten (...)
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  49.  44
    The mathematical modelling of tumour angiogenesis and invasion.M. A. J. Chaplain - 1995 - Acta Biotheoretica 43 (4):387-402.
    In order to accomplish the transition from avascular to vascular growth, solid tumours secrete a diffusible substance known as tumour angiogenesis factor (TAF) into the surrounding tissue. Endothelial cells which form the lining of neighbouring blood vessels respond to this chemotactic stimulus in a well-ordered sequence of events comprising, at minimum, of a degradation of their basement membrane, migration and proliferation. Capillary sprouts are formed which migrate towards the tumour eventually penetrating it and permitting vascular growth to take place. It (...)
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  50.  23
    Mathematical model for the calculation of resistance to heat transmission at the cross-flow of gas in tunnel ovens for the production of construction ceramics.K. Tahirbegović, Dimitrije Voronjec & N. Radojković - 1997 - Facta Universitatis, Series: Linguistics and Literature 4:409-421.
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